Average Error: 0.4 → 0.4
Time: 28.5s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\sqrt{k}} \cdot {\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{1 - k}{2}\right)}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{1}{\sqrt{k}} \cdot {\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{1 - k}{2}\right)}
double f(double k, double n) {
        double r3419087 = 1.0;
        double r3419088 = k;
        double r3419089 = sqrt(r3419088);
        double r3419090 = r3419087 / r3419089;
        double r3419091 = 2.0;
        double r3419092 = atan2(1.0, 0.0);
        double r3419093 = r3419091 * r3419092;
        double r3419094 = n;
        double r3419095 = r3419093 * r3419094;
        double r3419096 = r3419087 - r3419088;
        double r3419097 = r3419096 / r3419091;
        double r3419098 = pow(r3419095, r3419097);
        double r3419099 = r3419090 * r3419098;
        return r3419099;
}
↓
double f(double k, double n) {
        double r3419100 = 1.0;
        double r3419101 = k;
        double r3419102 = sqrt(r3419101);
        double r3419103 = r3419100 / r3419102;
        double r3419104 = n;
        double r3419105 = 2.0;
        double r3419106 = atan2(1.0, 0.0);
        double r3419107 = r3419105 * r3419106;
        double r3419108 = r3419104 * r3419107;
        double r3419109 = r3419100 - r3419101;
        double r3419110 = r3419109 / r3419105;
        double r3419111 = pow(r3419108, r3419110);
        double r3419112 = r3419103 * r3419111;
        return r3419112;
}

Error

Bits error versus k

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]

  2. Final simplification0.4

    \[\leadsto \frac{1}{\sqrt{k}} \cdot {\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{1 - k}{2}\right)}\]

Reproduce

herbie shell --seed 2019153 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))